tPareto: The truncated Pareto distribution

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

The truncated Pareto distribution

Description

Density, distribution function, quantile function and random generation for the truncated Pareto distribution.

Usage

dtpareto(x, shape, scale = 1, endpoint = Inf, log = FALSE)
ptpareto(x, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtpareto(p, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtpareto(n, shape, scale = 1, endpoint = Inf)

Arguments

x	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
shape	The shape parameter of the truncated Pareto distribution, a strictly positive number.
scale	The scale parameter of the truncated Pareto distribution, a strictly positive number. Its default value is 1.
endpoint	Endpoint of the truncated Pareto distribution. The default value is Inf for which the truncated Pareto distribution corresponds to the ordinary Pareto distribution.
log	Logical indicating if the densities are given as \log(f), default is FALSE.
lower.tail	Logical indicating if the probabilities are of the form P(X\le x) (TRUE) or P(X>x) (FALSE). Default is TRUE.
log.p	Logical indicating if the probabilities are given as \log(p), default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the truncated Pareto distribution is equal to F_T(x) = F(x) / F(T) for x \le T where F is the CDF of an ordinary Pareto distribution and T is the endpoint (truncation point) of the truncated Pareto distribution.

Value

dtpareto gives the density function evaluated in x, ptpareto the CDF evaluated in x and qtpareto the quantile function evaluated in p. The length of the result is equal to the length of x or p.

rtpareto returns a random sample of length n.

Author(s)

Tom Reynkens

See Also

Pareto, Distributions

Examples

# Plot of the PDF
x = seq(1,10,0.01)
plot(x, dtpareto(x, shape=2, endpoint=10), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x = seq(1,10,0.01)
plot(x, ptpareto(x, shape=2, endpoint=10), xlab="x", ylab="CDF", type="l")

TReynkens/ReIns documentation built on Nov. 30, 2024, 3:47 p.m.